Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion

被引：7

作者：

Qiao, Leijie ^{[1
]}

Qiu, Wenlin ^{[2
]}

Xu, Da ^{[2
]}

机构：

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

[2] Hunan Normal Univ, Sch Math & Stat, Changsha 410081, Hunan, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2023年 / 93卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Three-dimensional tempered integrodifferential equation; Trapezoidal convolution quadrature rule; ADI finite difference; compact difference methods; Convergence analysis; Numerical examples; ALGORITHM;

D O I：

10.1007/s11075-022-01454-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proposes and analyzes a tempered fractional integrodifferential equation in three-dimensional (3D) space. The Crank-Nicolson (CN) method and trapezoidal convolution quadrature rule are used to approximate the time derivative and tempered fractional integral term respectively, and finite difference/compact difference approaches combined with corresponding alternating direction implicit (ADI) algorithms are employed for spatial discretizations, which obtains the fully discrete CN ADI finite difference/compact difference schemes. Then, convergence analysis of two kinds of ADI schemes is derived via the energy argument and the generating function of Toeplitz matrices. Provided numerical examples confirm our theoretical estimates.

引用

页码：1083 / 1104

页数：22

共 50 条

[1] Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion
Leijie Qiao
Wenlin Qiu
Da Xu
[J]. Numerical Algorithms, 2023, 93 : 1083 - 1104
[2] A compact ADI Crank-Nicolson difference scheme for the two-dimensional time fractional subdiffusion equation
Li, Mingzhu
Ma, Qiang
Ding, Xiaohua
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (12) : 2525 - 2538
[3] THE CRANK-NICOLSON TYPE COMPACT DIFFERENCE SCHEMES FOR A LOADED TIME-FRACTIONAL HALLAIRE EQUATION
Alikhanov, Anatoly
Beshtokov, Murat G.
Mehra, Mani
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2021, 24 (04) : 1231 - 1256
[4] The Crank-Nicolson Type Compact Difference Schemes for a Loaded Time-Fractional Hallaire Equation
Anatoly Alikhanov
Murat Beshtokov
Mani Mehra
[J]. Fractional Calculus and Applied Analysis, 2021, 24 : 1231 - 1256
[5] 3D Crank-Nicolson finite difference time domain method for dispersive media
Rouf, H. K.
Costen, F.
Garcia, S. G.
[J]. ELECTRONICS LETTERS, 2009, 45 (19) : 961 - U10
[6] Crank-Nicolson finite difference scheme for the Rosenau-Burgers equation
Hu, Bing
Xu, Youcai
Hu, Jinsong
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 204 (01) : 311 - 316
[7] An optimized finite difference Crank-Nicolson iterative scheme for the 2D Sobolev equation
Xia, Hong
Luo, Zhendong
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2017,
[8] An optimized finite difference Crank-Nicolson iterative scheme for the 2D Sobolev equation
Hong Xia
Zhendong Luo
[J]. Advances in Difference Equations, 2017
[9] Modified Crank-Nicolson Difference Schemes for Nonlocal Boundary Value Problem for the Schrodinger Equation
Ashyralyev, Allaberen
Sirma, Ali
[J]. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2009, 2009
[10] Crank-Nicolson finite difference schemes for parabolic optimal Dirichlet boundary control problems
Yang, Caijie
Sun, Tongjun
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (12) : 7346 - 7363

← 1 2 3 4 5 →